As used herein, downmixing refers to the operation of deriving N output audio signals (or channels) from information encoded by M input audio signals (or channels), where 1≦N<M. Common expectations on high-quality downmixing include low information loss, compatible dialogue levels and high psychoacoustic fidelity between the input and output signals.
Downmixing frequently includes combining two signals into one, be it by waveform addition, transform-coefficient addition, weighted averaging or the like. While stereo-to-mono downmixing may be expressed by the simple relationship
                                          y            1                    =                                                    x                1                            +                              x                2                                                    2                                      ,                            (        1        )            general M-to-N downmixing may be written in matrix form as:
                              [                                                                      y                  1                                                                                    ⋮                                                                                      y                  N                                                              ]                =                                            [                                                                                                                                                              ⁢                                              a                        11                                                                                                  …                                                                              a                                              1                        ⁢                        M                                                                                                                                  ⋮                                                                                                                                                          ⋮                                                                                                              a                                              N                        ⁢                                                                                                  ⁢                        1                                                                                                  …                                                                              a                      NM                                                                                  ]                        ⁡                          [                                                                                          x                      1                                                                                                            ⋮                                                                                                              x                      M                                                                                  ]                                .                                    (        2        )            Here, the relative weight distribution between input channels contributing to a given output channel yk, as expressed by downmix coefficients ak1, . . . , akM, may follow from artistic considerations or may be related to the spatial layout of the reproducing audio sources. After fixing the relative ratios of the downmix coefficients, the gain of the downmixing may be determined by other concerns, notably energy conservation in cases where one input channel contributes to several output channels. In other situations, the priority may be to maintain a consistent dialogue level. This requirement makes it possible to join audio sections seamlessly together although they have been obtained by different types of mixing or encoding.
A difficulty frequently encountered in downmixing, whether the gain has been chosen by energy conservation or in response to a dialogue-level requirement, is that an output signal exceeds its permitted range. To avoid clipping the output signal or damaging the reproducing audio equipment, a common practice in the art is to reduce the gain, either locally—at or around a point in time where out-of-range values would otherwise be produced—or globally. Supposing that output signal yk is out of range, the overall gain may be limited as per
                                          [                                                                                y                    1                                                                                                ⋮                                                                                                  y                    N                                                                        ]                    =                                    γ              ⁡                              [                                                                                                    a                        11                                                                                    …                                                                                      a                                                  1                          ⁢                          N                                                                                                                                                ⋮                                                                                                                                                                          ⋮                                                                                                                          a                                                  N                          ⁢                                                                                                          ⁢                          1                                                                                                            …                                                                                      a                        NM                                                                                            ]                                      ⁡                          [                                                                                          x                      1                                                                                                            ⋮                                                                                                              x                      M                                                                                  ]                                      ,                            (        3        )            where 0<y<1 is a limiting factor. One may also reduce only the gain of the signals contributing to yk, by
                              [                                                                      y                  1                                                                                    ⋮                                                                                      y                  N                                                              ]                =                                            ⌊                                                                                          a                      11                                                                            …                                                                              a                                              1                        ⁢                        M                                                                                                                                  ⋮                                                                                                                                                          ⋮                                                                                                              a                                                                        k                          -                          1                                                ,                        1                                                                                                  …                                                                              a                                                                        k                          -                          1                                                ,                        M                                                                                                                                                        γ                      ⁢                                                                                          ⁢                                              a                                                  k                          ⁢                                                                                                          ⁢                          1                                                                                                                          …                                                                              γ                      ⁢                                                                                          ⁢                                              a                        kM                                                                                                                                                        a                                                                        k                          +                          1                                                ,                        1                                                                                                  …                                                                              a                                                                        k                          +                          1                                                ,                        M                                                                                                                                  ⋮                                                                                                                                                          ⋮                                                                                                              a                                              N                        ⁢                                                                                                  ⁢                        1                                                                                                  …                                                                              a                      NM                                                                                  ⌋                        ⁡                          [                                                                                          x                      1                                                                                                            ⋮                                                                                                              x                      M                                                                                  ]                                .                                    (        4        )            
Irrespective of how limiting factors are applied, the requirements of meeting the dialogue level and performing the limiting in a psychoacoustically unnoticeable manner are clearly contradictory. Limiting the gain more locally favours the consistency of the dialogue level but leads to more sudden and more perceptible gain changes. Similarly, performing the limiting over an extended time period improves one problem but worsens the other. Hence, there is need for improved downmixing techniques.